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There are 3 Red Books, 5 Green Books and 6 Blue Books on a shelf. In h
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25 Jun 2019, 05:04
25 Jun 2019, 05:04
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A
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Difficulty:
35%
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Question Stats:
74% (01:57) correct
26%
(02:23)
wrong
based on 129
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There are 3 Red Books, 5 Green Books and 6 Blue Books on a shelf. In how many ways can we pick two books without replacement such that both books have different colors?
A. 28
B. 63
C. 25
D. 52
E. 60
Experts please explain, what can be the possible ways to approach such questions?
A. 28
B. 63
C. 25
D. 52
E. 60
Experts please explain, what can be the possible ways to approach such questions?
There are 3 Red Books, 5 Green Books and 6 Blue Books on a shelf. In h
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Updated on: 25 Jun 2019, 06:32
Updated on: 25 Jun 2019, 06:32
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For books to have different colors, there are three ways:
red+green possibilities = 3*5 = 15
green+blue possibilities = 5*6 = 30
red+blue possibilities = 3*6 = 18
so the total ways = 15 + 18 + 30 = 63
IMO B
A reverse method can be done by calculating (the total ways of choosing two books) - (the ways of choosing similar books):
14C2 - (3C2 + 5C2 + 6C2) = 91 - (3+10+15) = 91 - 28 = 63
red+green possibilities = 3*5 = 15
green+blue possibilities = 5*6 = 30
red+blue possibilities = 3*6 = 18
so the total ways = 15 + 18 + 30 = 63
IMO B
A reverse method can be done by calculating (the total ways of choosing two books) - (the ways of choosing similar books):
14C2 - (3C2 + 5C2 + 6C2) = 91 - (3+10+15) = 91 - 28 = 63
Originally posted by MahmoudFawzy on 25 Jun 2019, 06:16.
Last edited by MahmoudFawzy on 25 Jun 2019, 06:32, edited 1 time in total.
Last edited by MahmoudFawzy on 25 Jun 2019, 06:32, edited 1 time in total.
General Discussion
Current Student
Joined: 16 Jan 2019
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GMAT 1: 740 Q50 V40 
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Re: There are 3 Red Books, 5 Green Books and 6 Blue Books on a shelf. In h
[#permalink]
25 Jun 2019, 06:31
25 Jun 2019, 06:31
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Kudos
Total Number of ways of picking two books = 14C2 = 91
Number of ways both books are red = 3C2 = 3
Number of ways both books are green = 5C2 = 10
Number of ways both books are blue = 6C2 = 15
Total number ways the two books are not the same color = 91-(3+10+15) = 63
Answer is (B)
Posted from my mobile device
Number of ways both books are red = 3C2 = 3
Number of ways both books are green = 5C2 = 10
Number of ways both books are blue = 6C2 = 15
Total number ways the two books are not the same color = 91-(3+10+15) = 63
Answer is (B)
Posted from my mobile device
